Abstract
The mechanical properties of polymer network structures dependmostly on the network rigidity. In very weakly cross-linkedsystems, entanglements also play a predominant role in themechanical properties, especially hardness; and the contribution ofentanglements competes with the contribution of the networkrigidity. The entanglement and the network rigidity both depend onchain length and its distribution. In this work, the chain lengthdistribution was affected by adding the cross-linker in lateperiods. The chain distribution was expressed by a mathematicalequation using probabilistic concepts. Hardness was expressed interms of a chain distribution probability function. It was modifiedto include the effect of the chain alignment for the polymers thathave alignment. It was found that scaling relations existed between(i) the cross-linker concentration `C', (ii) the molecular weightof the prepolymer that gives the maximum hardness (MWmax ),(iii) a parameter `k' that appears in the mathematical equation,and (iv) a parameter `g' that shows the contribution of chainalignment to hardness. Combined scalings with simple numericalpowers were also found among these parameters. The combined scalingk×MWmax ~C-1 holds true for both polymethylmethacrylate and polystyrene. It seems to be a universal relation.
Published Version
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